where \(\eta _k\)  refers to the \(k\) th modal eddy viscosity coefficient. In our current work, we formulate an RL framework to learn \(\eta _k(t)\) , and call this approach as multi-modal RL (MMRL). Although the proposed closure problem can be formulated using more traditional adjoint based [1]} or sensitivity based approaches [2]}, our chief motivation in this study is to explore the feasiblity of RL workflows for the ROM closure problems. More specifically, in this paper we aim to introduce a variational multiscale RL (VMRL) approach by formulating a new procedure to forge a reward function that does not require access to the training data. Our approach therefore facilitates new RL workflows since RL enhanced computational frameworks might play an integral role in designing many end-to-end data-driven approaches for broader optimization and control problems.
